Throughout R will represent a ring with unit element 1, and all modules will be unitary 7?-
modules. We call a module M a completely indecomposable module if the endomorphism …

MODULES WITH PERFECT DECOMPOSITIONS Page 1 MATH. SCAND. 98 (2006), 19^)3
MODULES WITH PERFECT DECOMPOSITIONS LIDIA ANGELERIHUGEL and MANUEL …

Direct summands of products Page 1 0003-889X/02/010012-12 $ 3.90/0 Arch. Math. 78 (2002)
12–23 Sonderdruck aus © Birkhäuser Verlag, Basel, 2002 Direct summands of products By LIDIA …

It is shown that, given a module M over a ring with 1, every direct product of copies of M is a
direct sum of modules with local endomorphism rings if and only if every direct sum of copies …

First we take a right artinian ring R. Then every injective. R-module E is a direct sum of
indecomposable modules. Further for every simple submodule S of Ey there exists a direct …

We have defined an additive category 3t induced from a family of completely
indecomposable modules {Mrt}, namely whose objects consist of directsums of MΛ and …

The initial problem in our discussion is to characterize those families (M&sK of modules over
an associative ring R with 1 for which the direct product nktK Mk is projective (R-modules are …

Let R be a ring and M a right R-module. Let σ [M] be the full subcategory of Mod-R
subgenerated by M. An M-natural class 𝒦 is a subclass of σ [M] closed under submodules …

74 GARCIA morphisms will be written as acting on the side opposite scalars. For a ring R, J
(R)(resp., Soc (R)) will denote the Jacobson radical (resp., the left socle) of R, and the left …

A saturated class Δ of modules is any class of nonsingular right 7?-modules closed under
direct sums, injective hulls, submodules and isomorphic copies. Saturated classes are used …